Question

Write the equation of the line that is parallel to 5x + 2y = 7 and contains the point (-2, -4). Express final answer in standard form.

Answer
A.5x + 2y = -18

B.5x - 2y = -2

C. 2x - 5y = 16

D.y = -5/2x - 9

Answer 1

Thanks in advance

Answer 2

I found it to be answer A. Would you like an explanation?

Answer 3

Yes
Thanks

Answer 4

I rewrote the given equation in slope intercept form.

5x + 2y = 7

2y = -5x + 7 (sub. 5x from both sides)

y = (-5/2)x + 7/2 (divide both sides by 2)

Right here is where you use the slope to find the line parallel.

Remember that if two lines are parallel, their slopes must be equal.

This means any equation modeled by y = (-5/2)x + b will be parallel to the original, where b is the y-intercept.

To find the line that passes through the point (-2,-4), substitute the respective x and y values into the general equation.

This gives (-4) = (-5/2)(-2) + b
-4 = 5 + b
-9 = b

Use this to find the specific equation of the line. Substitute b back in...

y = (-5/2)x - 9

That is the correct line, but not an answer you gave. In order to find which equation is the correct answer, multiply both sides by 2 to get 2y = -5x - 18

Now add 5x to both sides and voila! 5x + 2y = -18